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AP EAMCET · Maths · Hyperbola

If a circle of radius 4 cm passes through the foci of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{4}=1\) and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is

  1. A \(2\)
  2. B \(2 \sqrt{3}\)
  3. C \(\frac{2}{\sqrt{3}}\)
  4. D \(\sqrt{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2\)

Step-by-step Solution

Detailed explanation

Given that circle passes through foci of given hyperbola and have radius 4 . \(\therefore \quad c=4\) and \(b=2\) [ from equation of hyperbola] \(\because \quad a^2+b^2=c^2 \Rightarrow a^2+4=16 \Rightarrow a=2 \sqrt{3}\) For congugate hyperbola \(a=2\) and \(c=4\)…